In [1]} the number of edge modes was analyzed along \(k_x\in \mathbb {R}\)  for a fixed boundary condition \(a\ne 0\) . A more standard formulation of bulk-edge correspondence along the lines of [2]}, [3]} was shown to be violated. There, the counting of edge modes crossing \(\omega =\mu \)  is actually ill-defined, see [1]}, so that another definition for edge mode counting has to be used. Yet the system remains anomalous: the number of edge modes changes with \(a\) . The origin of the anomaly is rooted in the infinite region of the spectrum, as \(k_x\)  and \(\omega \)  go to infinity. Here instead, by restricting the parameters to a compact loop \(\mathcal {C}_R\) , the theorem above shows that the bulk-edge correspondence can be restored, provided we do not insist on a fixed value of \(a\) .
